For example, combustor inner tubes, transition pieces, turbine rotor blades, stator vanes, shroud segments (ring segments), etc., which are hot-parts constituting a gas turbine, receive varying thermal stress due to starting up and stopping while being exposed to high-temperature, high-pressure combustion gas, and thus are easily damaged due to high-temperature fatigue, thermal fatigue, and creep. In particular, turbine rotor blades are severely damaged because they receive a centrifugal force due to rotor rotation and a gas bending force due to combustion gas; therefore, strict maintenance and management are required. Accordingly, an inspection schedule is set at appropriate intervals; during inspection, parts are removed for inspection if required, and the parts are replaced or repaired depending on the degree of damage.
It is desirable to set long intervals between periodic inspections because, while carrying out an inspection, costs are required for disassembling and examining the gas turbine apparatus, and electric power cannot be generated. Therefore, there is a need for improving the durability of hot-parts for gas turbine and setting appropriate intervals between periodic inspections. There is also a need for reducing the costs and time required for repairing damaged hot-parts. In order to achieve this, it is required to relax the repair criterion such that small cracks that will not cause damage to an extent that function will be lost by the time of the next periodic inspection are allowed to be left unrepaired.
To fulfill the above-described needs, it is necessary to precisely predict the propagation behavior of cracks formed in hot-parts. For predicting the crack length in hot-parts, as disclosed in, for example, Patent Document 1 and Patent Document 2, methods have been proposed for observing the maximum crack length, etc., of the used part, predicting the stress and temperature on the basis of the result, and predicting the fatigue life on the basis of a master curve acquired through the predicted values and a test piece.    Patent Document 1:    Japanese Unexamined Patent Application, Publication No. HEI-10-160646    Non-Patent Document 1:    Japanese Unexamined Patent Application, Publication No. HEI-9-195795